176 BEI± SYSTEM TECHNICAL JOURNAL 



constant amplitude field (providing the high-frequency character- 

 istic of the receiver is flat over the range of frequency variation). 

 But when two or more distinct paths exist, the combination at the 

 receiver becomes complex. This is evident in curve (c) shown in 

 Fig. 23 which is a direct summation of (a) and (b), and in (d) which 

 is the envelope of (c). The amplitude is subjected to variations* 

 which did not exist at all in the original wave. 



We might set up an equivalent effect right at the receiver by con- 

 structing two small local oscillators having the same characteristics 

 as the transmitter oscillator. The two small rotating condensers 

 would be driven by the same motor but the rotor of one would be 

 shifted backward in phase relation to the other so as to simulate the 

 case of transmission lag over the longer path. The relative fre- 

 quency characteristics of the two may then be represented by curves Ci 

 and C/ in (a) of Fig. 22. 



The frequency of the signals arriving over devious paths at the 

 receiver may be put in the form of an equation as, 



F, = Fo+fsm[r{t-d,/V)l (6a) 



F, = Fo-\-fsm{r{t-d^/V)l (6b) 



wherein, 



Fo = the mean frequency 



/ = one-half the total variation 



r = 27r times the frequency of rotation of the condenser 



^= length of path 



F= velocity of waves. 



For a difference in length of path equal to 300 wave lengths at a 

 frequency of 600,000 cycles per second, for example, the time lag 

 of one wave behind the other will be equal to 300/600,000 second or 

 1/2000 second. The lag of one of the condensers behind the other in 

 the "equivalent" case described above would be then for 30 cycles 

 per second rotation of the condensers, 30/2000 times 360 degrees 

 or 5.4 degrees. The lag of 5.4 degrees represents the lag of the con- 

 denser rotor so that the frequency lag will depend entirely upon the 

 rate of change of frequency by the rotating condensers at any 

 given instant. 



Now to determine the resultant wave at the receiver we must know 

 both amplitude and relative phase of the components arri\ang over 

 the different paths. The amplitude will be constant, and we shall 

 assume known, although it may actually follow slow changes with 



